Conte broke Chelsea’s transfer record to bring in £60million striker Alvaro Morata from Real Madrid, but was keen to add another front man to his squad.
The Blues manager wanted a reunion with his former Juventus forward Llorente, but the Spaniard instead left Swansea for Tottenham.
And Conte is said to be frustrated by Chelsea’s efforts to sign Llorente.
According to The Times, Chelsea offered Swansea just £5million for Llorente – less than half the £11.5m Tottenham signed the 32-year-old for.
Conte initially asked Chelsea to sign Llorente back in January amid fears Diego Costa was set for a big-money move to the Chinese Super League.
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But the Chelsea board were unwilling to invest so much money into a player with little resale value and were also unsure about his mobility.
Conte is now left with just one striker in Michy Batshuayi after Morata picked up a hamstring injury against Manchester City before the international break, which could keep him out of action for the next two months.
However, the Italian clearly has reservations about the Belgian forward.
Conte refused to bring on Batshuayi as Morata’s replacement in the 1-0 defeat to City, instead opting for winger Willian.